Problem: Alice has a cute cat. To keep her cat fit, Alice wants to design an exercising walk for her cat! 

Initially, Alice's cat is located in a cell (x,y) of an infinite grid. According to Alice's theory, cat needs to move: 

  * exactly a steps left: from (u,v) to (u-1,v); 
  * exactly b steps right: from (u,v) to (u+1,v); 
  * exactly c steps down: from (u,v) to (u,v-1); 
  * exactly d steps up: from (u,v) to (u,v+1). 



Note that the moves can be performed in an arbitrary order. For example, if the cat has to move 1 step left, 3 steps right and 2 steps down, then the walk right, down, left, right, right, down is valid.

Alice, however, is worrying that her cat might get lost if it moves far away from her. So she hopes that her cat is always in the area [x_1,x_2]× [y_1,y_2], i.e. for every cat's position (u,v) of a walk x_1 ≤ u ≤ x_2 and y_1 ≤ v ≤ y_2 holds.

Also, note that the cat can visit the same cell multiple times.

Can you help Alice find out if there exists a walk satisfying her wishes?

Formally, the walk should contain exactly a+b+c+d unit moves (a to the left, b to the right, c to the down, d to the up). Alice can do the moves in any order. Her current position (u, v) should always satisfy the constraints: x_1 ≤ u ≤ x_2, y_1 ≤ v ≤ y_2. The staring point is (x, y).

You are required to answer t test cases independently.

Input

The first line contains a single integer t (1 ≤ t ≤ 10^3) — the number of testcases. 

The first line of each test case contains four integers a, b, c, d (0 ≤ a,b,c,d ≤ 10^8, a+b+c+d ≥ 1).

The second line of the test case contains six integers x, y, x_1, y_1, x_2, y_2 (-10^8 ≤ x_1≤ x ≤ x_2 ≤ 10^8, -10^8 ≤ y_1 ≤ y ≤ y_2 ≤ 10^8).

Output

For each test case, output "YES" in a separate line, if there exists a walk satisfying her wishes. Otherwise, output "NO" in a separate line. 

You can print each letter in any case (upper or lower).

Example

Input


6
3 2 2 2
0 0 -2 -2 2 2
3 1 4 1
0 0 -1 -1 1 1
1 1 1 1
1 1 1 1 1 1
0 0 0 1
0 0 0 0 0 1
5 1 1 1
0 0 -100 -100 0 100
1 1 5 1
0 0 -100 -100 100 0


Output


Yes
No
No
Yes
Yes
Yes

Note

In the first test case, one valid exercising walk is $$$(0,0)→ (-1,0) → (-2,0)→ (-2,1) → (-2,2)→ (-1,2)→(0,2)→ (0,1)→ (0,0) → (-1,0)$$$

Solution (in JAVA):

Solution:


import java.io.*;
import java.util.*;

public class codeforces
{
    static int M = 1_000_000_007;
    static int INF = 2_000_000_000;
    static final FastScanner fs = new FastScanner();

    //variable

    public static void main(String[] args) throws IOException {

        int T = fs.nextInt();
        while(T-->0) {
            int[] step = fs.arrayIn(4);
            int x = fs.nextInt();
            int y = fs.nextInt();
            int[] area = fs.arrayIn(4);
            if((x == area[0] && x == area[2] && (step[0] > 0 || step[1] > 0))
                    || (y == area[1] && y == area[3] && (step[2] > 0 || step[3] > 0))) {
                System.out.println("NO");
                continue;
            }
            int min = Math.min(step[0], step[1]);
            step[0] -= min;
            step[1] -= min;
            min = Math.min(step[2], step[3]);
            step[2] -= min;
            step[3] -= min;
            //System.out.println(step[0]+" "+step[1]+" "+step[2] +" "+step[3]);

            if (area[0] <= x - step[0] && x + step[1] <= area[2] && area[1] <= y - step[2] && y + step[3] <= area[3]) {
                System.out.println("YES");
            } else System.out.println("NO");
        }

    }
    //class

    //function

    // Template
    static int lcm(int a, int b) {
        return (a / gcd(a, b)) * b;
    }

    static int gcd(int a, int b) {
        if(a==0) return b;

        return gcd(b%a,a);
    }
    static void premutation(int n, ArrayList<Integer> arr,boolean[] chosen) {
        if(arr.size() == n) {

        }else {
            for(int i=1; i<=n; i++) {
                if(chosen[i]) continue;
                arr.add(i);
                chosen[i] = true;
                premutation(n,arr,chosen);
                arr.remove(i);
                chosen[i] = false;
            }
        }
    }
    static boolean isPalindrome(char[] c) {
        int n = c.length;
        for(int i=0; i<n/2; i++) {
            if(c[i] != c[n-i-1]) return false;
        }
        return true;
    }

    static long nCk(int n, int k) {
        return (modMult(fact(n),fastexp(modMult(fact(n-k),fact(k)),M-2)));
    }

    static long fact (long n) {

        long fact =1;
        for(int i=1; i<=n; i++) {
            fact = modMult(fact,i);
        }
        return fact%M;
    }

    static int modMult(long a,long b) {
        return (int) (a*b%M);
    }
    static int negMult(long a,long b) {
        return (int)((a*b)%M + M)%M;
    }
    static long fastexp(long x, int y){
        if(y==1) return x;

        long ans = fastexp(x,y/2);
        if(y%2 == 0) return modMult(ans,ans);
        else return modMult(ans,modMult(ans,x));
    }

    static final Random random = new Random();

    static void ruffleSort(long[] arr)
    {
        int n = arr.length;
        for(int i=0; i<n; i++)
        {
            int j = random.nextInt(n);
            long temp = arr[j];
            arr[j] = arr[i];
            arr[i] = temp;
        }
        Arrays.sort(arr);
    }


    public static class Pairs implements Comparable<Pairs>
    {
        long f,s;
        Pairs(long f, long s)
        {
            this.f = f;
            this.s = s;
        }
        public int compareTo(Pairs p)
        {
            return Long.compare(this.f,p.f);
        }

        @Override
        public boolean equals(Object o) {
            if (this == o) return true;
            if (!(o instanceof Pairs)) return false;
            Pairs pairs = (Pairs) o;
            return f == pairs.f && s == pairs.s;
        }

        @Override
        public int hashCode() {
            return Objects.hash(f, s);
        }
    }
}
class FastScanner
{
    BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
    StringTokenizer str = new StringTokenizer("");

    String next() throws IOException
    {
        while(!str.hasMoreTokens())
            str = new StringTokenizer(br.readLine());

        return str.nextToken();
    }

    char nextChar() throws IOException {
        return next().charAt(0);
    }

    int nextInt() throws IOException
    {
        return Integer.parseInt(next());
    }

    float nextFloat() throws IOException
    {
        return Float.parseFloat(next());
    }

    double nextDouble() throws IOException
    {
        return Double.parseDouble(next());
    }
    long nextLong() throws IOException
    {
        return Long.parseLong(next());
    }
    byte nextByte() throws IOException
    {
        return Byte.parseByte(next());
    }
    int [] arrayIn(int n) throws IOException
    {
        int[] arr = new int[n];
        for(int i=0; i<n; i++)
        {
            arr[i] = nextInt();
        }
        return arr;
    }
}